Pearson Edexcel International GCSE (9–1) · MATHEMATICS A · Unit
Unit 5
104 practice questions
Topics covered
Practice questions
11–17 of 17 · Hard
Question 11
5 marks · Hard
Answer and see the solution →Shape A has vertices at (–4, 1), (–1, 1), and (–4, 4). Shape A is enlarged by scale factor k about the origin to produce shape B, which has one vertex at (–8, 2).
(a)[2 marks]Find the value of the scale factor k.
(b)[3 marks]Write down the coordinates of the other two vertices of shape B.
Question 12
5 marks · Hard
Answer and see the solution →A club has 80 members. The table summarizes the ages of its members:
Age (years) Number of members 10–19 23 20–34 18 35–49 25 50–64 9 65–80 5 The mid-interval values for the age groups are: 14.5, 27, 42, 57, and 72.5 respectively.
(a)[3 marks]Estimate the mean age of the members. Give your answer to 1 decimal place.
(b)[2 marks]A member is chosen at random. Estimate the probability that this member is younger than 35 years old.
Question 13
6 marks · Hard
Answer and see the solution →A six-sided die is rolled 48 times. The frequencies for each face are shown below:
Face 1 2 3 4 5 6 Frequency 10 9 12 6 7 4 (a) Calculate the experimental probability of rolling a 5.
(b) If the die is fair, calculate the expected frequency of rolling a 5 in 48 throws.
(c) Based on the table, discuss whether the die is likely to be fair, giving a reason for your answer.
(a)[2 marks]Calculate the experimental probability of rolling a 5.
(b)[2 marks]If the die is fair, calculate the expected frequency of rolling a 5 in 48 throws.
(c)[2 marks]Based on the frequencies in the table, discuss whether the die is likely to be fair, giving a reason for your answer.
Question 14
7 marks · Hard
Answer and see the solution →The Venn diagram below shows the results of a survey of 100 students about whether they prefer football (F), hockey (H), or tennis (T).
Venn diagram of student sports preferences The numbers indicate how many students are in each region. The '?' represents the number of students who did not prefer any of these sports.
(a)[1 mark]Calculate the value of '?'.
(b)[2 marks]Find the probability that a randomly selected student preferred at least two of the sports.
(c)[2 marks]Given that a randomly selected student preferred hockey, find the probability that the student also preferred football.
(d)[2 marks]A student is chosen at random. What is the probability that this student preferred exactly one sport?
Question 15
7 marks · Hard
Answer and see the solution →An environmental scientist measures the length of a rectangular tank as 6.9 m to the nearest 0.1 m and the width as 4.0 m to the nearest 0.1 m. The height is exactly 3 m. Water is pumped into the tank at a constant rate, and the depth of water in the tank follows the quadratic equation where is in hours and is in metres.
(a)[2 marks]Calculate the lower and upper bounds for the length and width of the tank.
(b)[2 marks]Hence, calculate the lower and upper bounds for the cross-sectional area of the base of the tank.
(c)[3 marks]After 2 hours, the measured depth of water is 1.8 m. The scientist models the depth by the quadratic equation . Does the model fit the data at ? Show your working.
Question 16
6 marks · Hard
Answer and see the solution →A cumulative frequency diagram shows the results of a survey measuring the heights, in cm, of 80 students. The median height is 162 cm and the upper quartile is 170 cm. The heights have been recorded to the nearest centimetre.
(a)[1 mark]Write down the lower and upper bounds of the median height.
(b)[2 marks]If a box plot is drawn for the data, what is the minimum range of heights that could possibly be represented by the interquartile range? Give your answer to 1 decimal place.
(c)[3 marks]Calculate the lower and upper bounds for the proportion of students with a height strictly greater than 170 cm.
Question 17
7 marks · Hard
Answer and see the solution →The point P(2, 3) is transformed onto Q by a translation of and then by a reflection in the x-axis. The coordinates of Q are used as root values of the quadratic equation , where s and p are the sum and product of the coordinates of Q, respectively.
(a)[2 marks]Find the coordinates of Q after both transformations.
(b)[2 marks]Write down the values of s and p.
(c)[3 marks]Solve the quadratic equation for x.